Motor Temperature Rise Formulas
Motor winding temperature formulas: the hot temperature from the change in resistance, the temperature rise over the ambient and the insulation life rule.
The formulas
| To find | Formula |
|---|---|
| Hot winding temperature (copper) | T2 = (R2 / R1) × (235 + T1) − 235 |
| Temperature rise | ΔT = T2 − Ta |
| Insulation life factor (rule of thumb) | L = 2^(−ΔTover / 10) |
R1 is the winding resistance when cold, measured at the winding temperature T1 (equal to the ambient when the motor has rested), R2 the resistance measured hot, and Ta the ambient temperature at the end of the test, all in °C and ohms. The constant 235 is for copper in IEC 60034-1, and the constant for aluminium is 225. The resistance method gives the average temperature of the winding, and the hottest spot is higher. The life rule says that the insulation life halves for each 10 K above its rating. It is a common rule of thumb and not a guarantee. The limits of the rise depend on the insulation class and the standard, so use the figure on the nameplate. The values here are examples.
Worked example: a winding of 1.20 Ω at 25 °C that reads 1.46 Ω hot
The ambient at the end of the test is 30 °C.
- T2 = (1.46 / 1.2) × (235 + 25) − 235 = 81.33 °C
- ΔT = 81.33 − 30 = 51.33 K
Worked example: insulation life
- A winding 10 K over its rating has a life factor of 2^(−10 / 10) = 0.5
Life factor by temperature above the rating
| Above the rating | Life factor |
|---|---|
| 0 K | 1 |
| 10 K | 0.5 |
| 20 K | 0.25 |
| 30 K | 0.125 |
Frequently asked questions
Why measure the resistance?
The winding is inside the motor, so a thermometer cannot reach it. The resistance of copper rises in a known way with the temperature, so the resistance gives the average temperature.
Why does the winding need the cold reading?
The formula compares the hot resistance with a reference resistance at a known temperature. Measure the cold value after the motor has stood long enough to be at the ambient temperature.
Is the average temperature the hottest temperature?
No. The hot spot is higher than the average, and the limits of the standard allow for it.
What does the life rule mean in practice?
A motor that runs hot ages faster. The rule shows why a small excess of temperature over a long time matters, but the real life depends on the insulation system and the duty.
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